What is the sum of $1+2+4+8+16+ \cdots + 1024$?
Solution: This is a finite geometric series with first term 1, common ratio 2 and 11 terms. Thus the sum is: $$\frac{1(1-2^{11})}{1-2} = \frac{1-2^{11}}{-1} = 2^{11}-1 = 2048-1 = \boxed{2047}.$$